A Modified Approach to the Mathematical Model of Crack with Pre-destruction Zones

Abstract

Generalized Griffith’s criterion and models with pre-destruction zones are considered in this paper. Unlike those models that used linear dependences, the authors proposed the destruction process to be represented by differential equations. The positive effect of such representation is the possibility to formulate boundary conditions using the corresponding constant in the differential equation solution. The result is that the critical load values responsible for the occurrence and propagation of quasi-brittle cracks in materials are obtained. It is stated that the maximum load of crack propagation completely or essentially depends on its initial length. These generalizations estimate the influence of stress caused by hydrogen close to crack-like defects. In the case of defect-free material, the established formula is used to determine the critical forces necessary for the occurrence of cracks with a definite length. Numerical examples for some types of materials are given to illustrate the theoretical estimates.